/*- * Copyright (c) 2011 David Schultz * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. */ #include __FBSDID("$FreeBSD$"); #include #include #include "math_private.h" static const uint32_t exp_ovfl = 0x40862e42, /* high bits of MAX_EXP * ln2 ~= 710 */ cexp_ovfl = 0x4096b8e4, /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */ k = 1799; /* constant for reduction */ static const double kln2 = 1246.97177782734161156; /* k * ln2 */ double complex cexp(double complex z) { double x, y, exp_x; uint32_t hx, hy, lx, ly; int scale; x = creal(z); y = cimag(z); EXTRACT_WORDS(hy, ly, y); hy &= 0x7fffffff; /* cexp(x + I 0) = exp(x) + I 0 */ if ((hy | ly) == 0) return (cpack(exp(x), y)); if (hy >= 0x7ff00000) { EXTRACT_WORDS(hx, lx, x); if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) { /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ return (cpack(y - y, y - y)); } else if (hx & 0x80000000) { /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ return (cpack(0.0, 0.0)); } else { /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ return (cpack(x, y - y)); } } GET_HIGH_WORD(hx, x); if (hx >= exp_ovfl && hx <= cexp_ovfl) { /* * x is between 709.7 and 1454.3, so we must scale to avoid * overflow in exp(x). We use exp(x) = exp(x - kln2) * 2**k, * carefully chosen to minimize |exp(kln2) - 2**k|. We also * scale the exponent of exp(x) to MANT_DIG to avoid loss of * accuracy due to underflow if sin(y) is tiny. */ exp_x = exp(x - kln2); GET_HIGH_WORD(hx, exp_x); SET_HIGH_WORD(exp_x, (hx & 0xfffff) | ((0x3ff + 52) << 20)); scale = (hx >> 20) - (0x3ff + 52) + k; return (cpack(scalbn(cos(y) * exp_x, scale), scalbn(sin(y) * exp_x, scale))); } else { /* * Cases covered here: * - x < exp_ovfl and exp(x) won't overflow (common case) * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0 * - x = +-Inf (generated by exp()) * - x = NaN (spurious inexact exception from y) */ exp_x = exp(x); return (cpack(exp_x * cos(y), exp_x * sin(y))); } }